Examples of volumetric measuring devices include kitchen measuring cups and rain gauges.
To use a volumetric measuring device, the user first puts contents into the vessel or otherwise causes the contents to be measured to accumulate in the vessel (e.g., placing a rain gauge outside to collect falling rain). Next, the user estimates the vertical level of the contents and translates that into a volume estimate. In the case of many translucent kitchen measuring cups, the estimate and translation is done by raising the vessel so that the top of the contents is at eye level, and then matching the top of the contents with line markings on the side of the vessel indicating specific volumes. The reading of vertical level and translation can alternatively be done by other electronic or mechanical means.
When estimating the vertical level of the contents, there will be error in the estimate. There are many sources of error. Examples include: (1) Variation in level of the contents across the surface of the contents; (2) Variation in the level due to inconsistently accounting for the height of the meniscus of the liquid; and (3) When visually estimating the vertical level relative to markings on the side of the vessel, not being perfectly perpendicular to the surface of the contents and the side of the vessel. This introduces error due to the thickness of the sides of the vessel.
Error in estimating the vertical level of contents, when multiplied by the surface area of the contents, translates into an error in the volume measurement, which is termed ‘error volume’, below. When evaluating measurement error, typically the user is interested in the relative error—that is, the error volume relative to the volume of contents being measured.
Many sources of error in estimating the vertical level of contents are present over the entire operational range, i.e., whether the vessel is almost full or almost empty.
A problem with existing volumetric measurement devices is that the absolute error volume does not decrease adequately as the volume of contents decreases. Therefore, the relative error, that is, the error volume as a fraction of the volume being measured, becomes larger when measuring a small amount of contents (e.g., measuring ¼ cup in a 2-cup measuring cup). The problem is partly because the error in estimating the vertical level may not decrease adequately when measuring a smaller volume of contents. The problem is also partly because the surface area of the contents may not decrease adequately. This increase in relative error when measuring small volume of contents typically becomes unacceptable, forcing the user to utilize an alternative measuring device.